Qryrnnnr" _f 16l?4rr ir4ccttr,4l- €'4x'rsr'*' u> nn-p"'{a) "na'l 0r * i'trtrte-/52,'zc'ry s,r;;...,-1.ftlrna&t,tg f not sg'e'l;c tu uYi / 'n unybe I Aft! g'{1t&t-iin, w'Y| *P#:{:Experiment tt ;s *n{*";; Meazu,ues the BoltzmannConstant7 phr*:ey, rcn*(of ;-&re I f,tvttn A" t+,mp(de Stuffn<r 't* be l& titk uf e sara&,T)z lafn November15, 2013 "l:il"u'f ' k*' v"({vza? be''r''u*'ffi'uf":l':::+vn'd i'rehar ' '|- on/t1 U';'lftS(S.z By using a diode we were uUf.ftp construct a circuit from which we measureddifierent voltages. Flom these measurements we were able io he value of the Boltzmann constant ".Ul* shocklerlp*e "rffirl lnilrt lesbt& ? thtt)4 Theory 0c/,r tqhn g,t ? ,/ In this exlerimelwe measuredthe valueof the Boltzmann ^rrby $n ideal diodeequation11] | ,./a0od I : Io(""v/ktT- r). .z , using the Shockley (i) \"/ Jaact , This a.llowedus to relate the current through the diode to the voltage acrosst\yi{ode. In i. *n" current though the diode, 1o is the reversesaturation current, e is the this equatiorfi -v fundamental element of cha,rge, I/ is the voltage across lhe diode,, 7 is i the temperature inside .//'"r/ 7{tne diode,andksis the Boltzmannff.nstant ,Y , . Ae iq6{nu'w"'( ' " ' ' r v ' \ J t!{r'd tuLw c'n/ vuL4"\ cculil krs r-tt L'l 'rf AVOfL*t*utn A (,Uoltttrg/;nftorl,*,y'tnn ' ut qv tnJde 'lS/,llfu ).s €,xt'rtulJ hZ ind,dee/ " f*lotiyut;^ m*ti',nt1n ouutor fttttttlr'C/.h\ Cuu{c(t'L Method Y( Stttrcl' Pa pt"e'rsand Mat eri{2,v" \,/ 8tfueiltnpntriay ' -,t ,.i / .' r/" fuh,G, ,rJ^ ( tlttvt/ewvT w*re we rec,,(q il&{rt {ot re?41 il,*/,y i * //4/)"'Y-(e""( "74y rcc4 rnaft#ads" Lv)tA /rtq//\r'tt6''/>' t'vtfA JWe measured the voltage at two different points in the circuit (Fig. 1) using a Hewlett Packard an uncertaintvof + 0.005V.By meaMult'i,meter 972A which gaveour voltagemeasurements 6il;n //eA*'unpno,,u) o4ingnno*4ilt is ''P';tY u ill (wt'c\;s#wtrutil yx6^.t,i*674ffi(r{rmny4sfi5 cn t|'p yr"Jh a",t ex/{a)nttp;f@, Ya /t^aW 16gt",rS " I7e4 hqre rliyera"1 I {t(cisiut. (, Slvtl"lrt |cte /*a Swi+c */r(', fu r"pxw{4 s u,tdtr<?aa/, figu'e. ilrePlaa'd Fywe cef+,"s -t5 ld $lena dtb,'(ed '. )u"eltt yu{€ k'ufe lx&v'rL(6 wu{t( b4 .It t"t"ta( reaalert t*fo ffi;{rq' *t *;'fr , be4 rud fl,,tres*>,Atvrytlws ft'f4 t i, ,*,t4+ wA'V fut,d,;,3' ;&tJ* {A}1; Atran!,rfu1> Et{fi.3Si{l ts rfiet*r pin ffi-l ts r*€tsr rtrta d iocfu- Y P^rtrf it u'ts (,;[b; ;dul e1/t^ avtaxt ;( )rt 2lahruTtbn ezpLiln (,.1d;1in &w fi,urt*^ lowcan suring ihe voltdg6 at two points we were able to indirectly measurethe voltaqe 1;' i c'-+1 \dAr.,'. a,nd crrrrent through throush the the tr9(tot trail#tor. the current andthe ttuffitor, ,"; H t 4tvr(\ / CtVl / &LYrD ./\ mdirectly . t measured the voltage across the @i"€q[ya --;V -:--- ,r tk fihni,su( ,t' '/\ /r((a*a( /' ryrdss the *u4, 4 t';(A Bv measurinethe voltase utYoint f'lw" "5lu*u% dW -' jwittr respect to groundby-bhranrsee'f- ?rfi nt ; t c@t t1 i , , vn -vt. "'i )'r|*rr",i' ,,,,/r';i' vlrf& t/ ,r 't., ,,I t ?zttv Tl l::" Royr&Htk ,/io/,t7furoi,t r. -/^ Ot'Lrre&" fltS[ fll (ntvT / " ': , s b/4 f 'kt*4 of l o''^t A had to usea LF356 op-ampcurrentTo measuretne@d6'W.frrough the transistor uli{* /. e 7, voltageconverterbecausethis curryllli,trmall. This madeit possibleto havea readablevoltage. WA-A{ By measuringthe voltageat point B,Vs,we wereableto indirectlymeasurethe currentthrough ,:O:: ::'*n*, :f^*c'szamqc4, by using thetransistor 1r, uYrtrc{- t"$i{yA V: fi ,^,pryc,sc*Xi'" o''"f':'u:""ii'*'t 90"1 of the 1 ko pot. L{lke*;5 ,rpr*,# ffi*{<c.ge alteredtheresistance We also assumed that the voltage across the diode will make "evlksT )> 1 so we were able to -t": approximatethe current through the diode t":? , I x loeev/keT . '', 2 :t;ry#, tk /,A ffg^* Vo(.{c,gZtan,^d*f */,e Smao/'&tt4.e,"t.e*n h*,n €t,s(r{l)ra preers€lq w,frhovtbe/nq/,sAriU ti o{ e&tf&{ 4 *At-neattrer',d4 T ' ou.{, . ;g;;i$nt{- i i4 ,-11, e L'A/Fi 1'' t)wtt/1 , jr;Lw(, i= 4"ol y ; "+ 7 /,tco/4rn /.rtr'L J t L.-) t,{-r ;. ''-f h",vvp,'tt\ .) luWu rt'e(trt li,tv Avr.Tzqrt'ttrl We are able to assumethis by starting out measuredvoltageat point A at approximately-0.6V. From this we can seethat the current will be on the ora", of b)@Junicn make this approximation valid. F}om this we obtained m# " thevottage v: LnI:#-tfgr". rnship betweenl6yI and r\ttn_>ltrj,,I . [-rl,r,'ir.rr, (,t),'t'-., ,,1i, ,r\""4{4Yiui ' , _ . . , , " "'{oi'trutari1p' ,' _+., ')'^F'"';'9'"')'.'.' vv6ri k615,"or-g/,,"(,,"t:":K:!!:f":i;J,L:l ;-":,; e'-- 1\\.. is large enoughto /Ai [ ,ietz.W,\,t";r(+ 1 ;, , , , - 6 t ' E - 1,r=---1rii" this' ' /p,r- ki: -!/;), ,.r,:.k.1 We measuredthe resistorRl to be g.gg7+0.002 kfl usinga Stanford,ReaserchSR 7115meter. 1V,tk,/; {,{{/s:;t ,t(;i{rrr,.z-, ,/ PB-503"Protoboard"C'ircu'it We createdthe circuit ona GlobalSpeci,alti,es Boardy![&,gna]_y'lit:k-,/*,q t/r-t Generator and used BNC Coaci,alCables to connect the multimeter's to the Protoboard. We LrlL,tltr*, . ^ - * 't- rgnoredthe resistancean4 c4ficrtance of the BNC cablgr"cables.During the experimentwe v,' v Ur' tuh,r,h p1,iyg -Luh.,_/r.i)r,,rt ^ ,:;i.,-ti,,r ,r4Vq"' | : ,ttlXr,tiun(i1 used a 2NSg04 transistor instead of a diode and assumedthE transiAtoi''would act as a perfect F'z tl'r;, (d:/'' -._--i -_--j -l/,u 1rr.t,.:,/,:5.,1 would stay under f .),.,;,, la,; ;.v-1,of thesevoltagesw to n{}ne W**#E-u#*"ururements l/ tvt'lpf y',ft':1ri ' t rl ft;a l-*, the saturationvoltage. ,!-t l,' ,,/ t-t -'" i:;gt Ltyt )'( {v|'i'1/v1v' 7:f'4La7ir -'' / We made the assumptionthat the temperatureinsideof the transistorwill be approximately diode. We : I i n''' fir1rilV'r. J( equalto room temperaturf],rri"t we havemeasured ro u"d+ - 0.5 K usinga mercuryther,),"'l/t'^ 'url U f,u d.. . , . .!l ,.,t+,, / trbZ i ; ' r ! ',1t,''''|u\t,r1'l'.".mometer.ThevoItag.ru'"ntheop_ampwaSmeaSu,"t}+.os+0.005Vand.ftlo,"+ryyLin./ ,ti,,,,\ L,i t*'J flrt w tnevoltage gi1t1ial5fffiand " ; + 0,005v. Wealso * i), i,' l,/ik:I\ to be -14.94 thecircuitwasmeasur.ed nl+ry^ui, assumedtheelementoffundamentalchargeetobeexactlyl.64xl0-1eCl3]. 6iA rto-'k, :,if.= ]Co(- t ._,u,ti,5tt4 .: , t"t'(l'u"t'rtr:/.* t,LLpL, w!;,;t;:'y,{:':,':,{;,,#, ',,''*"?,;': ni'li'i'' r&ll/Resurts ,),:,"1)"n ,-".':,:,:;;i!;J;,"-),i' :;o!r'; i^":,' -. *:* ":""-, '" -:'" ";","" tt- *-, ":- -: .. ll : hrt' Jt ;f -* f f -------ll*\ y. ^. L :",, :" /l(t".u, ',/ we expectedin Eqn. 5. The SravI;fT\8. 2 is a semi-logplot of the current through the diode I ._ ='' dt'zt / /rr, versusthe voltageacrosstrre {$r.d. We wereable to plot the data in Matlab using the program Y Flom the measurement,-JdL,"*" fopnd that the relationshipbetween tgql and,Vvrur'lin"ui u, i, , , , 5t ,j( T'l , {.t,i.( ulQ \/ ' Boltzmann co\gbdnt. The/reducel ch'i-squaredof our measurementsis 874.88. Our measured Y: ) j': - ::- 't n(6n ? - ll'L; wtwlt"n"{ \''c lYtwt Lt c'Botrr*unn ;'> /(;r i)< 10-'J J/K. The known r.r,o''rrvalue rr.ll". constant,kB-"*., wasmeasured t" b"(;;1+'0.,i6)"lo3?'liN"i'rr" (i,ttlo,a6) ( X,iit _ I ."i/'''l) 1-**-**e 'ilitakt qrh'/'tt"7t:'/ ' 61Ll"pd!1 We;'"e r* al tv':"s f,,,d lt-ls tftte f-ti:t/7 L'i*l' ,vtt-,.wo,rh -!r^'Jrtttt'l;;';: t }'4k',r,'at' i t"'{t"@t*'( Ls i76tu{t't d",tfui i,,*o * O-, ^:,,!*i ' hl fi$":"l/" ' trf't5 't4L*"e'1r'|a''tat z ,r"'kv 1,,*r,{t,i,,, ,'i t),;'.ult 4k: i ) *iln $N.t- #xp l$r,,t alu-t llat h) ,re/t ahz tlna( 4 t* is rzez-.ta ,i I Figure 2: Semi-logplot of Current versusVol 41.103x+-34.1056 ds,F.1_988q delb= 1^2847 -* of the Boltzmann constantis ,be:l3aT1O-23 J lKlS]. Although the value for the known value \)gtnute ev are both on the same ^ v{uY of the Boltzmann constant does not lav within our *,tei,in discrepancyis most likely due to only havetwo significantfiguresfor ggggt$acsitudg-This ,.4n1,r,&':'4 the voltagesmeasuredwhich causedus to have multiple data points for one uortage./-i''it;'''''' Su r ' * ' ., , I i''"dyp- '? vt,hi;tnr'lhyq ci*4* 1"t)'4 ? C [. (tle- tl*lnhrn '= ()' i 7 7 /]1d/t4 t rlrt J'ii lpa''t (rnuf tae,ffrd^*) t;' y{,;*lm5l,rJ,,?t:tw14 P-t' ^/'.L )rn, = b"l' +ut ?l"t^ alnw"Wl f i" v( tL's95"'if't'*C1 ] a A'bv ) fts)trrnd "',':^t,'!',|)",iff; ,y.srt*/ o) /)1ce{lj, f/'it +,01 +,0t ) d (itr'!l),'eort/' av "s FL*' rew 4f -tu ni rtt€6iar*ti {y.7,;,rT,#'"/)'n:^"::' w^ro'ut:r'r hvyt,rtr! i+ .')nrrtcn.rt r"ur",iclr ,b.,s.tl|;' p*}'&o^*!,1-e,|eo(,t*.( D,,t ('A' "n ,J4 tiln /.|4 {,/!J fvf}€Je,{ *^4 v$o;'eyn(-tco-'{ \ pt',t *nu,*;4 r! tL |i#.,:J , :* C4;sc'efwg l,*,ro *9 tLrtbtt'< awfudvr, ryY=7/0, H ,it uihdi,,gSt,m,n*eo:. bo"t'tr whicAis n* is uval hotcl , 7looy r\;stnPa^ry tl"an"'0\-Uda,ei'Y W!!'9:'' / ydw nzt4 * la hul 4 ef W b(a,r a/^/^< ),,yuotvd ,/ *V w/.,p-tfur<2, onaf ,,uh"r{ ?a.nk References sr'^&" Sle! pos)*'*e. ,: /n-v +- ,-f^"(t''"e con rLs2ayt^ [1] A. Sedra,K. Smith: MicroelectronicCircuits. 4th ed. New York, New York: Oxford, 1998. p132-134 \ '/ / [2] J. Lockhart, W. Man: {t n,-at;y Pur( Advanced Lab l- Manual and S-upplementary information. Version F13, San Flancisco,CA: San FlanciscoState University 2013.p76-82 [3] R. Eisberg,R. Resnick: Quantum Physicsof Atoms, Molecules,Solids,Nuclei, and Particles,2nd ed. United State of America: John Wiley & Sons,Inc. 1985. 6llYv Uz /"4u1€/ +r^ o/.,/2,'pefb's pafiT , A4 g{4 ca'4 ce(
© Copyright 2024 Paperzz